Lee-Yang zeros of periodic and quasiperiodic anisotropic XY chains in a transverse field

The partition function zeros of the anisotropic XY chain in a complex transverse field are studied analytically and numerically. It is found that the partition function zeros of the periodic and quasiperiodic quantum Ising chain lie on the circle at zero temperature and the radius equal to the values of the critical field. For the periodic and quasiperiodic anisotropic XY chains, the closed curves are split to two or three closed curves as the anisotropic parameter gamma decreases at a given ratio of two kinds of exchange interactions. For the isotropic XX case, the partition function zeros lie on the straight segments which are parallel to the real axis and the segments move towards the real axis as the temperature goes to zero.     

Stabilization of periodic and quasiperiodic motion in chaotic systems through changes in the system variables

This work deals with the suppression of chaos in dissipative systems that exhibit a transition from the coexistence of several periodic oscillations to deterministic chaos. The application of changes in the system variables is able to yield the prechaotic behaviour, that can be either quasiperiodic (two inconmensurate frequencies) or periodic (frequency locking), in the same way as for the original system. The performance of the method is shown by application to the two-dimensional Burgers map.     

Equation of solvated ion oscillations in solution under an external periodic electric field

An equation describing ion oscillations with respect to solvent molecules is derived as a result of the consideration of the interaction of an external electric field with free and bound charges in the volume of a salt solution in a polar dielectric liquid. An analysis of the equation shows that the ion motion represents a drift toward one of the electrodes forming the field in the electroinsulated solution volume if amplitudes and durations of sinusoidal field half-periods are different.     

Painleve property of anharmonic systems with an external periodic field

The Painlevé property of anharmonic systems with an external periodic field is investigated. This property tell us that the only movable singularities exhibited by the solutions are poles. The Painlevé property can serve to distinguish between integrable and nonintegrable systems.     

On the contactless effect of an electric field on liquid systems

An effect of an electric field on the evaporation of polar and nonpolar liquids (water and a hydrocarbon, respectively) is established. The effect is stronger in the former case.     

Irrational mode locking in quasiperiodic systems

A model for ac-driven systems, based on the Tang-Wiesenfeld-Bak-Coppersmith-Littlewood automaton for an elastic medium, exhibits mode-locked steps with frequencies that are irrational multiples of the drive frequency, when the pinning is spatially quasiperiodic. Detailed numerical evidence is presented for the large-system-size convergence of such a mode-locked step. The irrational mode locking is stable to small thermal noise and weak disorder. Continuous-time models with irrational mode locking and possible experimental realizations are discussed.     

Mathematical analysis of ion motion in a gas subjected to an alternating-sign periodic asymmetric-waveform electric field

The motion of ions in a gas subjected to an alternating-sign periodic asymmetric-waveform electric field is mathematically analyzed based on solving the continuity equation. Solutions to the transfer equation are found that describe the ion distribution in the gas in planar and cylindrical cavities. The effect of ion focusing arising in the spatially nonuniform field is evaluated. The analytical results may be helpful in designing ion mobility increment spectrometers—instruments that detect microadditives of explosives, drugs, and other hazardous materials.     

Ising model in a quasiperiodic transverse field,percolation, and contact processes in quasiperiodic environments

Quantum Ising models in a transverse field are related to continuous-time percolation processes whose oriented percolation versions are contact processes. We study such models in the presence of quasiperiodic disorder and prove localization in the ground state, no percolation, and extinction, respectively, for sufficiently large disorder.     

Radiation of an electron in an electric field

By the methods of classical theory, the motion of an electron in the field of a longitudinal electric wave is analyzed. This field may be taken as a model of the accelerating field at the axis of a linear accelerator. It was shown that the radiation of electrons in this field is analogous to the radiation in a constant homogeneous electric field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 96–99, May, 1976.The authors are sincerely grateful to Prof. V. A. Bagrov for formulating the problem and for his constant interest in the work.     

Transport properties of graphene under periodic and quasiperiodic magnetic superlattices

We study the transmission of Dirac electrons through the one-dimensional periodic, Fibonacci, and Thue–Morse magnetic superlattices (MS), which can be realized by two different magnetic blocks arranged in certain sequences in graphene. The numerical results show that the transmission as a function of incident energy presents regular resonance splitting effect in periodic MS due to the split energy spectrum. For the quasiperiodic MS with more layers, they exhibit rich transmission patterns. In particular, the transmission in Fibonacci MS presents scaling property and fragmented behavior with self-similarity, while the transmission in Thue–Morse MS presents more perfect resonant peaks which are related to the completely transparent states. Furthermore, these interesting properties are robust against the profile of MS, but dependent on the magnetic structure parameters and the transverse wave vector.     

Chemical interaction in peroxide-metal systems in the regime of combustion in an external electric field

The effect of a contactless electric field on the interactions involved in the combustion of the BaO₂-Fe and MnO₂-Fe systems is studied. The results are indicative of the possibility of increasing the extent of chemical conversion during the combustion of oxide systems by applying an external electric field. A possible mechanism of the influence of an electric field on the redox processes occurring during the combustion of oxide systems composed of a metal fuel and a solid oxidizer is described.     

Comment on “painleve property of anharmonic systems with an external periodic field”

We show that the result of Steeb and Kunick concerning the singularity structure of the Van der Pol equation is false.